Правка раздела «Solution»

crico правка от 27 дек. 2024 г., 21:05

правка #12598 предыдущая #12596 ← раньше позже →

en/5.4.17.md +3 −1

			### Statement

			$5.4.16*.$ [Insert problem description here]

			__Example Statement__:
			$1.1.1.$ Between two flat parallel plates located at a distance δ from each other, there
			is a monatomic gas (the free path of atoms is much longer than δ). Estimate
			the heat flux density if the temperature of the plates is maintained at T and
			T + ∆T, respectively, and the unit volume of gas contains n' atoms; µ is the
			mass of the atom


			### Solution

			[Your solution should be placed here]

			__Example Solution__:
			Heat flow is defined by


			$$J =\frac{ΔE}{A*t} $$

			We know that the change of the energy is given by

			$$ΔE = \frac{nRΔT}{\gamma-1}$$

			Where (n) is the number of moles

			We know that Heat flow then

			$$J = \frac{nRΔT}{(\gamma-1)A*t}$$

			We know that the time is given by because (the free path of atoms is much longer than δ) furthermore λ>>δ therefore the average collision between the molecules will be δ:

			$$t = \frac{δ}{v}$$

			Likewise:

			$$J = \frac{nRΔTv}{(\gamma-1)A*δ}$$

			Now we have to:

			$$A*δ=V$$

			So from the previous equations we have to:

			$$J = \frac{nRΔTv}{(\gamma-1)V}$$

			Another way to write this equation is:

			$$J = \frac{n'KΔTv}{(\gamma-1)}$$
		@@ -52,7 +52,9 @@Solution

			Where (n') is the number of the atoms

		−	$$v=\
		+
		+
		+	How ΔT<<T is much less than this

			#### Answer

			[Insert a concise answer or boxed result, like this:]


			__Example Answer__:
			$$ x(t)=\frac{bt^3}{6} $$
		ещё строк без изменений 5

	### Statement		### Statement

	$5.4.16*.$ [Insert problem description here]		$5.4.16*.$ [Insert problem description here]

	__Example Statement__:		__Example Statement__:
	$1.1.1.$ Between two flat parallel plates located at a distance δ from each other, there		$1.1.1.$ Between two flat parallel plates located at a distance δ from each other, there
	is a monatomic gas (the free path of atoms is much longer than δ). Estimate		is a monatomic gas (the free path of atoms is much longer than δ). Estimate
	the heat flux density if the temperature of the plates is maintained at T and		the heat flux density if the temperature of the plates is maintained at T and
	T + ∆T, respectively, and the unit volume of gas contains n' atoms; µ is the		T + ∆T, respectively, and the unit volume of gas contains n' atoms; µ is the
	mass of the atom		mass of the atom


	### Solution		### Solution

	[Your solution should be placed here]		[Your solution should be placed here]

	__Example Solution__:		__Example Solution__:
	Heat flow is defined by		Heat flow is defined by


	$$J =\frac{ΔE}{A*t} $$		$$J =\frac{ΔE}{A*t} $$

	We know that the change of the energy is given by		We know that the change of the energy is given by

	$$ΔE = \frac{nRΔT}{\gamma-1}$$		$$ΔE = \frac{nRΔT}{\gamma-1}$$

	Where (n) is the number of moles		Where (n) is the number of moles

	We know that Heat flow then		We know that Heat flow then

	$$J = \frac{nRΔT}{(\gamma-1)A*t}$$		$$J = \frac{nRΔT}{(\gamma-1)A*t}$$

	We know that the time is given by because (the free path of atoms is much longer than δ) furthermore λ>>δ therefore the average collision between the molecules will be δ:		We know that the time is given by because (the free path of atoms is much longer than δ) furthermore λ>>δ therefore the average collision between the molecules will be δ:

	$$t = \frac{δ}{v}$$		$$t = \frac{δ}{v}$$

	Likewise:		Likewise:

	$$J = \frac{nRΔTv}{(\gamma-1)A*δ}$$		$$J = \frac{nRΔTv}{(\gamma-1)A*δ}$$

	Now we have to:		Now we have to:

	$$A*δ=V$$		$$A*δ=V$$

	So from the previous equations we have to:		So from the previous equations we have to:

	$$J = \frac{nRΔTv}{(\gamma-1)V}$$		$$J = \frac{nRΔTv}{(\gamma-1)V}$$

	Another way to write this equation is:		Another way to write this equation is:

	$$J = \frac{n'KΔTv}{(\gamma-1)}$$		$$J = \frac{n'KΔTv}{(\gamma-1)}$$
	@@ -52,7 +52,9 @@Solution

	Where (n') is the number of the atoms		Where (n') is the number of the atoms

	$$v=\

			How ΔT<<T is much less than this

	#### Answer		#### Answer

	[Insert a concise answer or boxed result, like this:]		[Insert a concise answer or boxed result, like this:]


	__Example Answer__:		__Example Answer__:
	$$ x(t)=\frac{bt^3}{6} $$		$$ x(t)=\frac{bt^3}{6} $$
	ещё строк без изменений 5